There's no issue using prayer beads (Tasbeeh) for zikr, it is used only for counting, likewise there are many other modern electronic devices are available for counting, which can be used.
Imam Yahya bin Ma'een رحمہ اللہ said:
كان يحيى معه مسباح، فيدخل يده في ثيابه، فيسبح.
Imam Yahya bin Sa'eed al Qattani used to have a prayer beads (tasbeeh) which he use it with his hands under his garment.
[Tareekh Ibn Ma'een ba riwayah ad Dawri 4/314]
Allama ibn Allan رحمہ اللہ reports from Hafiz Ibn Hajar رحمہ اللہ that
زعم انها بدعة غير صحيح.
Considering Bidah to use a Tasbeeh is not correct.
[Al Futuhaat e Rabbaniyah 251/1]
Hafiz Suyuti رحمہ اللہ writes:
لم ينكل عن احد من السلف ولا من الخلف المنع من جواز عد الذكر بالسبحة، بل كان اكثرهم يعدونه بها ولا يرون ذلك مكروها.
It is not proven from salaf or khalaf that they deemed it impermissible to do zikr on tasbeeh, though they used tasbeeh for zikr and never said that it is makrooh (disliked).
[Al Hawi lil Fatawa 2/7]
Allama Ibn Aabideen Shami Hanfi رحمہ اللہ writes.
لا باس باتخاذ السبحة لغير رياء.
No issue to use tasbeeh if there's no intention of showing off.
[Fatawa Shami 650/1]
Allama Abd ar Rauf Manawi رحمہ اللہ writes:
Nothing has been proven from salaf and khalaf that it is makrooh (disliked) although it is recommended if a person uses it by heart with sole intention to indulge himself in zikr whilst letting other know at the same time, now there comes those people who do not concentrate while using tasbeeh and they use it without whole heartedly as they talk with others listen to the talks from here and there while using tasbeeh, their hands just are moving the beads and their heart and tongues are soaked in the worldly affairs, hence the actions of these kind of people are more likely to be condemned and it is from the most disliked "makroohat".
[Faiz ul Qadeer Lil Manawi 355/4]
Saydna Saad ibn Abi Waqas رضیﷲ عنه went to a woman with Rasool صلی اللہ علیہ وسلم who had some date's seeds or pebbles from which she was doing Tasbeeh.
إنّہ دخل علی مع رسول اللّٰہ صلّی اللّٰہ علیہ وسلّم علی امرأۃ وبین یدیہا نوی أو حصی، تسبّح بہ
[Sunan Abi Dawood 1500, Sunan Tirmidhi 3568, Musnad Sa'ad 88]
Imam Tirmidhi رحمہ اللہ said hadith is Hasan Gareeb and Imam Ibn Habban رحمہ اللہ said Sahih, furthermore, Hafiz Ibn Hajar رحمہ اللہ said Hasan in [Nata'ij Al Afkar 1/81]
The sanad of this narration is Da'if, The narrator named Khayzmah is "Majhool ul Haal" (Unknown) only Imam Ibn Hibban رحمہ اللہ mentioned him in [Al Thiqat 6/268]
~Translated from an Article of Shaikh Ghulam Mustafa Zaheer.
